Origamic metal-organic framework toward mechanical metamaterial

Origami, known as paper folding has become a fascinating research topic recently. Origami-inspired materials often establish mechanical properties that are difficult to achieve in conventional materials. However, the materials based on origami tessellation at the molecular level have been significantly underexplored. Herein, we report a two-dimensional (2D) porphyrinic metal-organic framework (MOF), self-assembled from Zn nodes and flexible porphyrin linkers, displaying folding motions based on origami tessellation. A combined experimental and theoretical investigation demonstrated the origami mechanism of the 2D porphyrinic MOF, whereby the flexible linker acts as a pivoting point. The discovery of the 2D tessellation hidden in the 2D MOF unveils origami mechanics at the molecular level.

and ethyl bromoacetate (10.6 mL, 100 mmol) were dissolved in 100 mL of acetone.The solution added to anhydrous potassium carbonate (13.8 g, 100 mmol) was reacted for 8 hours at 70 °C using reflux.
After the reaction, all solution was removed by using a rotary evaporator and extracted with H2O/CHCl3.

Synthesis of TCMOPP (5, 10, 15, 20-tetrakis [4-carboxymethyleneoxyphenyl] porphyrin):
TEMOPP (0.2 g, 0.195 mmol) was refluxed with sodium hydroxide (67 mg, 1.675 mmol) and H2O of 2 mL in MeOH of 20 mL for 4 hours.After then, the solvent was removed by using a rotary evaporator.4 mL of 0.5 N HCl solution was added to a crude product.After protonation, the color of the precipitate is green.The product was filtered, washed with water, and dried.The green product was dissolved in 600 μL of pyridine for neutralization of porphyrin and pyridine was removed by a rotary evaporator.
Then, the final product was washed with water, filtered, and dried under a vacuum (94 %). 1
Empirical dispersion corrections D3 by Grimme and coworkers were added, with Becke-Johnson damping. 8For the basis set, cc-pVDZ was used. 9The structure of the isolated aryloxy group was specified with internal coordinates including α and φ.The scan was made adiabatically in increments of ∆α = ∆φ = 1° within the ranges.
Elastic constants.Quantum mechanical calculations were performed based on density-functional theory (DFT) using the VASP program. 10For DFT calculation, Perdew-Burke-Ernzerhof exchangecorrelation functional 11 was used with the plane wave cutoff of 500 eV.Further, DFT-D3 dispersion correction with Becke-Johnson damping function was used. 12The initial molecular configuration was constructed from the experimental X-ray crystal structure which contains 1,208 atoms in a unit cell with a volume of 1.3 × 10 4 Å 3 .First, geometries as well as lattice parameters were optimized at -point since the unit cell is reasonably large.The optimized lattice parameters with DFT are a = 21.158Å, b = 23.866Å, c = 27.677Å, α = 98.622˚,  = 104.977˚,and  = 103.696˚,implying similar crystal structure with the experimental X-ray crystal structure (Supplementary Table 1).In the cartesian coordinate, the optimized cell parameters are represented as a = (21.16,0.0, 0.0), b = (−5.65,23.19, 0.0), and c = (−7.15,−6.01, 26.05) in Å.
In addition, elastic constants were obtained by calculating total electronic energies to external distortions from the ElaStic program 13 .Using Voigt notation, the relation between Lagrangian strains ηi and stresses τi can be written as where Cij is the stiffness tensor of material properties.Triclinic materials have 21 independent elements: C11, C12, C13, ⋯, C66 and 21 independent distortions, Di (i = 1, ⋯, 21) to lattice vectors were applied to determine these elements.Detailed information about the distortion and the energies of a strained crystal can be found in the literature. 13For the DFT method, 17 points for each distortion were used and the maximum Lagrangian strain is 0.04.Further, second order of elastic constants and energy choose as a method of calculation for the evaluation of elastic constants.From the above distortions Di, Cij's were obtained based on polynomial fittings to the energies of a strained crystal.Polynomial functions are well fitted to the data points.There are the calculated stiffness components (Cij's) in the GPa unit,  Furthermore, the stability of the crystal was checked by using the fact that the strain energy (Cijηiηj) must be positive-definite, calculating the determinants of the elastic stiffness constants matrices.PPF- Young's modulus and Poisson's ratio can be simply calculated from bulk (B = 1/2(BV + BR)) and shear (G = 1/2(GV + GR)) moduli using the assumption that the material is isotropic.There are two representations according to the values of bulk and shear moduli, and these are expressed by With the calculated elastic stiffness constants, the spatial dependence of elastic moduli and Poisson's ratio were analyzed from the ELATE software. 14Maximum and minimum values, as well as anisotropy (A) for Young's modulus, linear compressibility (β), shear modulus, and Poisson's ratio, were obtained.
Linear compressibility is defined as a reciprocal number of the Bulk modulus; thus, it has a unit of 1/TPa.Anisotropy is defined as a maximal value of the elastic moduli divided by a minimal value.
When the value becomes negative, the anisotropy is expressed to infinity.
In addition, Young's modulus (E), Poisson's ratio (ν), shear modulus (G), and bulk modulus (B) can be obtained in terms of Cij's or Sij's.For the calculation of bulk and shear moduli; Voigt and Reuss